I have some additional information to follow up on your question.

Martial Liber de Spectaculis 7 says:

Qualiter in Scythica religatus rupe Prometheus assiduam nimio pectore pavit avem, nuda Caledonio sic viscera praebuit urso non falsa pendens in cruce Laureolus. vivebant laceri membris stillantibus artus inque omni nusquam corpore corpus erat. denique supplicium (dignus tulit: ille parentis) vel domini iugulum foderat ense nocens, templa vel arcano demens spoliaverat auro, subdiderat saevas vel tibi, Roma, faces. vicerat antiquae sceleratus crimina famae, in quo, quae fuerat fabula, poena fuit.

Which translates:

As Prometheus, bound on Scythian crag, fed the tireless bird with his too abundant breast, so did Laureolus, hanging on no sham cross, give his naked flesh to a Caledonian bear. His lacerated limbs lived on, dripping gore, and in all his body, body there was none. Finally he met with the punishment he deserved; the guilty wretch had plunged a sword into his father’s throat or his master’s, or in his madness had robbed a temple of its secret gold, or laid a cruel torch to Rome. The criminal had outdone the misdeeds of ancient story; in him, what had been a play became an execution.

This seems to be the only reference to Caledonians bears in the arena (I found one book claiming Plutarch had also mentioned it, but the source had "forgotten" the citation and a search of texts found nothing).

I have a few points of interest, since I do work on Martial. But I will admit straight out I do not work on the ancient exotic animal trade, so I cannot speak to the realities of catching and transporting bears - please spare me mods.

First off, while the live bear trade question is up in the air, there are a few other reasons why Martial would have put in the word "Caledonio" whether or not that was the real origin of arena's bear. 1)it bears a striking similarity to the word "Calydonian" as in Calydonian boar which gives it a kind of heroic greatness 2) Caledonia is really far away and one of Martial's goals in the liber de spectaculis is to emphasize just how awesome the emperor was and how far his reach went - even if the Romans were not able to catch and import a real Scottish bear, they might have passed off another animal as Caledonian as part of the propaganda surrounding the games.

Another thing is this epigram describes one of the notorious mythological executions from the Roman arena in which a criminal was dressed up like a figure from myth and then executed accordingly. Martial describes a "Hercules" burned alive on a pyre, an "Orpheus" ripped up by beasts, a "Pasiphae" that I am not going to explain, etc. This "Laureolus" was a character from a mime (not that sort of mime), a robber who was crucified and then his body was torn apart by beasts. The Romans would probably not have needed a very ferocious bear to eat a guy who was already tied up and dying - just a hungry one. So I'm not sure that this is evidence that Romans thought the best bears for animal fights came from Caledonia.